Broad question to help in finding an appropriate method. So I have a given feature set of (DNA/genetic) predictors and a group of individuals which are either cases or controls for diseaseX. While I can build a classifier from the predictors (DNA), not everyone with diseaseX is genetic case of diseaseX, some are, but others are environmental subtypes. So basically the actual cases are split into cases that can and cannot be predicted by genetics, but there is no way of knowing which is which is in the cases. I am curious if there is a way to find the algorithm that predicts the cases that are also best predicted by the features I have. I.e. I want to create a predictor that works for predicting the genetic subtype, when I don't know which cases are due to genetics (but know some are). Any ideas on the best algorithms to begin tackling this problem? Or areas that have had similar problems that I can learn from?